International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 36, Pages 2315-2326

Cm solutions of systems of finite difference equations

Xinhe Liu, Xiuli Zhao, and Jianmin Ma

Department of Mathematics, Guangxi University, Nanning 530004, China

Received 25 February 2002

Copyright © 2003 Xinhe Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Let be the real number axis. Suppose that G, H are Cm maps from 2n+3 to . In this note, we discuss the system of finite difference equations G(x,f(x),f(x+1),,f(x+n),g(x),g(x+1),,g(x+n))+0 and H(x,g(x),g(x+1),,g(x+n),f(x),f(x+1),,f(x+n))=0 for all x, and give some relatively weak conditions for the above system of equations to have unique Cm solutions (m0).